Sketch and identify the path traced by the point P(x, y) if x = 1+. y =1- t> 0.

Q: Find the length of the curve y = x³/2 from (1, 1) to (2, 2/2).

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Q: ) Find the orthogonal trajectory of the family of curve given by y = In(r³ + b)

A: First formulate a differential equation to eliminate the parameter b . Then replace (dy/dx) by…

Q: |-*^= 39. What is the length of the curve y = √x- between x = 0 and x = 2?

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Q: Consider the curve segments: 1 - to x = 4 and 3 1 to x = $1: y = x² from x S2: y = Vx from x = = 16.

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Q: Find the point (a, b) on the graph of y = ex where the value ab is theleast.

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Q: Find the orthogonal trajectory of the given family of curves. (x^2)+4xy+(y^2)=c

A: Given family of curve                                               x2+4xy+y2=c we have to find…

Q: Find the orthogonal trajectory of the given family of curves: 1. у%3DG;(sec x + tan x)

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Q: Now compute [(x − 3y² + 2) ds where C' is the union of the curves C1 and C2. C1 is the line segment…

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Q: Find the exact length of the curve. y2 - 16(x + 4)3, Osxs 2, y > 0

A: The given equation of the curve is y2=16x+43, 0≤x≤2, y>0. The graph of this curve in the interval…

Q: The graph, when the curve y=v(3+ x^2 ) from x = 0 to x = 4 is rotated about x - axis is ....

A: This question can be solved using the concept of volume of solid generated when curve is rotated…

Q: A circle has a center at the origin and has a radius of R. If x = 10 and y = 20, determine the slope…

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Q: Find the exact length af te of the curve, 2. x-

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Q: Find the exact length of the curve. y = In(1-x), 0sxs 8.

A: Given that: y=ln 1-x2, 0≤x≤18

Q: C is polygonal path from (0, 0) to (3,0) to (3, 2); the sur- face is f(x, y) = 2x +y

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Q: Find the orthogonal trajectory of the family of curves x² + y² Cx

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Q: Find a path c(t) that traces the line y = 2x + 1 from (1, 3) to (3, 7) for 0 ≤ t ≤ 1.

A: Given:

Q: Find the orthogonal trajectory of the given family of curves. y=c*e^(2x)

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Q: Determine whether the work done along the path C is positive, negative, or zero. y O positive…

A: Consider that the sign of the work depend on the orientation of the path C. here the circulation can…

Q: (A) Evaluate" [(x² + y)dx + (x+1+d along the path ABCA shown in figure C(0,3) A(0,1) x=3sint y=3cost…

A: What is Line Integral: When we integrate a function along a straight line or a curve inspite of…

Q: Find the orthogonal trajectory to the family of curves: y(x²+1) = Cx

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Q: The line that is normal to the curve x2 + xy - 2y? = 0 at (3,3) intersects the curve at what other…

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Q: Trace the curve r2 = 4cos etan2e. %3D

A: The given equation is r2=4cos4θtan2θ. Simplify r2=4cos4θtan2θ as follows:…

Q: Find the length of the curve given by S(x) = (a -) defined on the interval (1, 2].

A: Consider the given curve:

Q: Mike found the orthogonal line to the curve f (x) =- 3sin( zx) +1 at x=-1. In which step did he…

A: The objective is to state the step in which he made an error while calculating orthogonal line to…

Q: Find the orthogonal trajectory of the given family of curves: 1. y = C (sec x + tan x) 2. x = C,es*…

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Q: Determine whether the work done along the path C is positive, negative, or zero. y

A: The work done along the path C is

Q: Let C be the curve y = x³ – 3x2 + 4x – 1 joining the points (1, 1) and (2, 3). Find the value of…

A: We need to find value of integral.

Q: Find the length of the curve y=z from z 0 to z=4.

A: The length of the curve is given by:

Q: Find the exact length of the curve. y = In(1 - x²), o s x s

A: Solve the problem using definite integral

Q: Trace the curve r = sinocos'o. 2)

A: Given: r=12sin3θcos3θ Explanation: r=12sinθcos3θat θ=0r=12sin0cos30=0⇒r=0at…

Q: Explain why a cubic Bézier curve is completely determined by x(0), x (0), х(1), and x'(1).

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Q: Let C be the curve connecting (0,0,

A: Given that C be the curve connecting  (0, 0, 0) to (1, 4, 1) to (3, 6, 2) to (2, 2, 1) to (0, 0, 0).…

Q: 2. Use the guidelines to sketch the curve. Y In x x²

A: The given function is: y=ln xx2 Note that the domain of the function is (0,∞). First of all, let's…

Q: Find the orthogonal trajectory to the family of curve given below y²=x²(1-Cx)

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Q: 3- Find the length of the curves in Exercises 1-4. X = (y3/2/3) - y¹/2 from y = 1 to y = 9

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Q: Consider the implicitly defined curve xy? +3x2 = 4. %3D Verify that the point (1, 1) is on the…

A: Consider the following curve: xy2+3x2=4 Substitute x=1 and y=1 in the above curve:…

Q: Find the orthogonal trajectory of the given family of curves: 1. y = C(sec x + tan x)

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Q: Find the exact length of the curve. y = x2 - In(x), 1 < x < 4

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Q: ind the equation of a line tangent to the circle x2 + y2 - 8x -14y + 52 = 0 at point (7,5) a.…

A: we have the equation of circle is  x2+y2-8x-14y+52=0  .........(1) differentiate with respect to x

Q: Evaluate (x-y+z-2)ds where C is the straight-line segment x=t, y= (1-t), z=1, from (0,1,1) to…

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Q: (b) Show that the points of inflexion of the curve y = (x- a) (x – b) lie on the | line 3x +a =4b.

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Q: The length of the curve y from x=0 to x= 6 is

A: We need to find the length of the curve  y=23(x2+1)32 from x=0 to x=6

Q: Consider the path equation r = (cos(t), t) = cos(t)ˆx + tyˆ.    For which time value t ∈ (3π/2,…

A: The radius of curvature at each point of the curve, ρ:ℝ→ℝ, is given by:ρ=r'3r'2r"2-r'·r"2…

Q: oves from origin at the curved Path -³x) m

A: Concept used: Velocity is the derivative of position with respect to time. Acceleration is…

Q: Find the paths orthogonal to the family of curves: cy ^ 2 = xe ^ x

A: Orthogonal path is a curve if it cuts every member of a given family of curves at right angles.

Q: 3. In Eercises, verify that the given point is on the curve and find the lines that are Haltangent…

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Q: analyze and trace the given curve y = x / (1 - x)2

A: To solve the following problem